The core of the tight polyhedral model presented here follows Kuiper's original drawings quite closely. Starting with this initial projective plane, the top and bottom are cut off and a tube added around the outside of the object to complete the tight immersion of the projective plane with one handle.

The following pages describe the relationship between Kuiper's drawings and the polyhedral level sets in more detail:

- Level 1: The initial circle.
- Level 2: Pulling one side across.
- Level 3: The initial self-intersection.
- Level 4: Adding the triple point.
- Level 5: The critical level.
- Level 6: After the critical level.
- Level 7: No more intersection.
- Level 8: The final circle.

* 8/10/94 dpvc@geom.umn.edu -- *

*The Geometry Center*